Answer:
The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.
Step-by-step explanation:
Given, f(x) = x⁴ + x³- 2 x².
Now, f(x) to touch or cross x-axis, f(x) must be equal to 0.
⇒ f(x) =0 ; x⁴ + x³- 2 x² = 0;
⇒ x²(x²+x-2) = 0
⇒ x=0 or x=-2 or x=1 .
now, for f(x) to touch x-axis, f'(x) = 0 at these three points(x=0,-2,1). where f'(x) is first derivative of x.
as f'(x) will be 0 if local maximum or minimum exists, thus touches the axis.
Now, f'(x) = 4 x³+ 3 x² - 4 x;
and only when x=0; f'(x) = 0.
⇒ The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.
Answer:
The original price was $2.
Step-by-step explanation:
The muffin is on sale for 5% off. This means it is being sold for 95% of its original price.
Its sale price is $1.90. This means that 95% of its original price is 1.90.
Let's set up an equation.
95% of original price is $1.90.
0.95 • x = 1.90
Divide both sides by 0.95 to isolate x.
x = 2
The original price was $2.
Hope this helps!
You could find the surface area using two different methods, but coming out with the same answer.
Method One: This method involves using an equation that helps finding the surface area for a square pyramid.
The equation: A+(1/2)ps=SA; we should break down what the letters stand for. A=Area of the base; the area of the base is 10×10=100 P= perimeter of the base; 10×4=40 S= Slant height;14
Let's put these values into the equation and find the surface area. 100+(1/2)(40)(14)=100+(20)(14)=100+280=380 The surface area is 380 in².
Method Two: The picture below shows how to lay out the square pyramid so you can find the area of each the shapes, then add them up. There are four triangles and a square.
Triangles: We use the equation (1/2)BH; let's plug the values in. 1/2(10)(14)=1/2(140)=70; there are four triangles, so let's multiply by four to find the area of all four of them triangles together. 70×4=280
Square: It's the side length squared. 10²=100; let's add everything together.
The four triangles+the square= the surface area
280+100=380
So, the surface area is 380 in².
Answer:
142°
Step-by-step explanation:
90°+52°= 142°
180°-142°= 38° (angles in a triangle add up to 180°)
x= 180°- 38° (angles on a straight line is 180°)
x= 142°
Answer:
90km/h in m/s will be
90×1000m/3600s ( convert 1km/1h to 1000m/3600sec )
=> 25m/s