Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x=12
- Equation x^2+p*x+q=0
-
Equation 4,3x-3,5=2,5x+1,9
-
Equation sin(x)=5/2
- Express {x} in terms of y where:
- -12*x+10*y=2
- -11*x-15*y=-7
- -6*x-6*y=-20
- -9*x-10*y=-20
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Identical expressions
- ctgx/ seven =- four / seven
- ctgx divide by 7 equally minus 4 divide by 7
- ctgx divide by seven equally minus four divide by seven
- ctgx divide by 7=-4 divide by 7
-
Similar expressions
- ctgx/7=+4/7
ctgx/7=-4/7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cot{\left(x \right)}}{7} = - \frac{4}{7}$$
transform
$$\frac{\cot{\left(x \right)}}{7} + \frac{4}{7} = 0$$
$$\frac{\cot{\left(x \right)}}{7} + \frac{4}{7} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{7} = - \frac{4}{7}$$
Divide both parts of the equation by 1/7
We get the answer: w = -4
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\frac{\cot{\left(x \right)}}{7} = - \frac{4}{7}$$
transform
$$\frac{\cot{\left(x \right)}}{7} + \frac{4}{7} = 0$$
$$\frac{\cot{\left(x \right)}}{7} + \frac{4}{7} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{7} = - \frac{4}{7}$$
Divide both parts of the equation by 1/7
w = -4/7 / (1/7)
We get the answer: w = -4
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
-acot(4)
$$- \operatorname{acot}{\left(4 \right)}$$
=
-acot(4)
$$- \operatorname{acot}{\left(4 \right)}$$
product
-acot(4)
$$- \operatorname{acot}{\left(4 \right)}$$
=
-acot(4)
$$- \operatorname{acot}{\left(4 \right)}$$
-acot(4)
Numerical answer
[src]
x1 = -53.6520537741534
x2 = -15.9529419310758
x3 = 28.0293552191813
x4 = 34.3125405263609
x5 = 6.03820664405272
x6 = 78.294837676618
x7 = -97.6343509244105
x8 = 53.1620964478996
x9 = 50.0205037943098
x10 = -37.9440905062044
x11 = -59.9352390813329
x12 = 94.0028009445669
x13 = 100.285986251747
x14 = -75.6432023492819
x15 = 72.0116523694384
x16 = 56.3036891014894
x17 = -81.9263876564615
x18 = -100.775943578
x19 = 15.4629846048221
x20 = 81.4364303302078
x21 = 12.3213919512323
x22 = -31.6609051990248
x23 = -9.66975662389624
x23 = -9.66975662389624