Find the measure of the marked angles.

Mathematics

1 answer:

Andre45 [30]3 years ago

4 0

So you have 6x-20 and 4x+30. These angles are perpendicular to each other, meaning together they equal 180 degrees. To solve for this equation add both of the equations together equal to 180.
6x-20+4x+30=180
Now subtract: 30-20= 10 so 180-10= 170
Next add 6x to 4x= 10x
So 170=10x
X=17
Now we use substitution to simplify our answers into numerical form:
6(17)-20= 82 this is for 6x-20
4(17)+30= 98 this is for 4x+30
Hope that helps! :)

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The linear density of a rod of length 4 m is given by (x) = 2/sqrt(x), in grams per centimeter, where x is measured in centimete

lyudmila [28]

The density of a substance is the ratio of its mass and its volume. The mass of the rod is 10,666.67 grams or 10.67 kgs.

<h3>What is the density of a substance?</h3>

The density of a substance is the ratio of its mass and its volume. Therefore we can write,

$d = \dfrac{m}{v}$

mass of substance = m kg

density of substance = d kg/m³

volume of that substance = v m³

The length of the rod is 4 meters, therefore, the length of the rod in centimeters will be 400 centimeters. Thus, The mass in terms of density can be written as,

$m = \int_0^4(2\sqrt x)dx\\\\$

$= [2\cdot \dfrac{2x^{\frac32}}{3}]_0^{400}\\\\= [\dfrac{4x^{\frac32}}{3}]_0^{400}\\\\=[\dfrac{4(400)^{\frac32}}{3}]-[\dfrac{4(0)^{\frac32}}{3}]\\\\= 10,666.\bar6\rm\ grams$